The club said Schuerrle trained on Monday, as did Cole who has been out since sustaining a rib injury against Norwich City on Oct. 6.
"Jose Mourinho believes tomorrow's game has come just too soon for the left back and he has remained in the UK," Chelsea said on their website.
Apart from long-term absentee Marco van Ginkel, Mourinho has no fresh injury concerns.
Schalke top Group E after winning two from two, ahead of Basel and Chelsea, both on three points. Steaua Bucharest have yet to pick up a point.